2021-2022 / GEOL1042-1

Geological imaging and inverse modeling


30h Th, 10h Pr, 30h Proj.

Number of credits

 Master of Science (MSc) in Geological and Mining Engineering5 crédits 


Language(s) of instruction

English language

Organisation and examination

Teaching in the second semester


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The course is divided into two parts: a first dedicated to inverse modeling, and a second one to teledetection and image analysis.
"Inverse modeling"
For each problem, review of fundamental geophysical equations (eg wave equation, eikonal equation, Poisson equation, Laplace equation, Maxwell's equations) using integral representation and differential methods for geophysics.
Linear and nonlinear inversion:
1. Method of Backus and Gilbert
2. Singular values decomposition
3. Regularization (Tikhonov, Occam, maximum entropy, total variation)
4. Iterative methods in ray tomography
Geo-Imaging will cover:
1. Introduction to Image Analysis and Stereology / The importance of vision in geosciences
2. From minerals to roxels : basic principles of scientific imaging in geosciences. Image calibration From analog to digital images Digital image file formats
3. Physics of Remote Sensing : Sources of electromagnetic radiation Atmospheric corrections, calibration methods Spectral properties of minerals, rocks and soils VNIR and SWIR ranges Multispectral, superspectral and hyperspectral remote sensing
4. Technologies for Core-Scanning
5. Technology of Earth Observation : Airborne and spaceborne platforms and sensors. Available systems (Landsat TM and ETM+, SPOT 3-4-5, ASTER, IKONOS, QuickBird, Sentinel, HyMap)
6. Image Processing : Image processing operations (global vs. local) Linear filters (low-pass, hi-pass, gradients) Mathematical Morphology (erosion, dilation, opening, closing)
7. Image analysis and processing, optical VNIR SWIR and thermal domains. Preprocessing. Geometric corrections, georeferencing. Radiometric correction, calibrations, atmospheric corrections  Multispectral data processing.  Data fusion, image sharpening Band ratios, indexes
8. Spectral Image Classification : Data transforms: principal components analysis, spectral classification techniques
7. Quantitative mineralogical and textural analysis: Modal (phase) and porosity analysis. Blob analysis: particle size and shape analysis. Texture indices

Learning outcomes of the learning unit

Part "Inverse modeling":
How does one obtain a physical model from a finite set of noisy observations? How to assess image appraisal ? How can a 2D models represent a 3D problem? The course of "Modeling and inversion in geophysics" presents the theory and algorithms necessary to find the answers to the questions raised above. The resolution of direct and inverse problems will be exposed for linear models and non-linear theory, according to a deterministic and Bayesian approach. Particular attention will be paid to numerical, mathematical and statistical aspects in relation with geophysical applications.
Many exercices will be resolved in Matlab, where students can create their own codes and test them on actual data (eg Deep Ocean Drilling vertical seismic profiling). Several practical cases will be solved through software commonly used in geophysical prospecting companies or equivalent (eg Mag3D, Grav3D, EM1DFM, Res2dinv).
Part "Teledetection and image analysis":
To give students a full overview of image processing and analysis in the geosciences To familiarize students with the main techniques for image acquisition and image processing with a particular emphasis on mathematical morphology To give students the possibility to practice digital imaging and develop their critical perception of applications in geology To provide guidelines for selecting appropriate hardware and software tools to solve a given problem.

Prerequisite knowledge and skills

GEOL0021-7 Geophysical Prospecting or equivalent
Matrices and Linear algebra
Introduction to numerical methods or numerical analysis

Planned learning activities and teaching methods

For the "inverse modeling"part:
The lab work will occur at each lecture after presentation of the theory. For some lab, a report must given for the following week per team of 2 students. The labs required a laptop, Matlab, as well as different geophysical softwares which will be provided.
For the "geo-imaging part":
Students will be given a case study and will have to provide results of image calibration, registration, classification, etc. using open source software provided by the professor

Mode of delivery (face to face, distance learning, hybrid learning)

Face to face with hands on programming

Recommended or required readings

Slides available on ecampus and reference textbook for the inversion part:    Parameter estimation and inverse problems by Aster et al.    
Supports didactiques mis à disposition sour forme pdf (cf portail) PIRARD E., SARDINI P., Image analysis for advanced characterization of geomaterials, EMU Lecture Notes, 2009 PIRARD, E., 2004, Chapter IV. Image measurements in P. FRANCUS (Ed) "Image analysis, sediments and paleoenvironmental reconstruction", Kluwer, NY PIRARD, E. et CACERES, F., 2004, Télédétection et télégestion des informations géologiques : de nouvelles technologies au service du développement. L'exemple du Sud Lipez (Bolivie).

Assessment methods and criteria

The final note will be a weighted average of both parts.

Work placement(s)

Organizational remarks